TSTP Solution File: GRP123-9.003 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP123-9.003 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:25:04 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 40 ( 24 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 68 ( 38 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 49 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(element_1,plain,
group_element(e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164527472,plain,
group_element(e_1),
inference(rewrite,[status(thm)],[element_1]),
[] ).
fof(element_2,plain,
group_element(e_2),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164531512,plain,
group_element(e_2),
inference(rewrite,[status(thm)],[element_2]),
[] ).
fof(product1_total_function1,plain,
! [A,B] :
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164570736,plain,
( ~ group_element(A)
| ~ group_element(B)
| product1(A,B,e_1)
| product1(A,B,e_2)
| product1(A,B,e_3) ),
inference(rewrite,[status(thm)],[product1_total_function1]),
[] ).
fof(product1_right_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164591312,plain,
( ~ product1(A,B,C)
| ~ product1(A,D,C)
| equalish(B,D) ),
inference(rewrite,[status(thm)],[product1_right_cancellation]),
[] ).
fof(product1_idempotence,plain,
! [A] : product1(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164599288,plain,
product1(A,A,A),
inference(rewrite,[status(thm)],[product1_idempotence]),
[] ).
cnf(173603920,plain,
( ~ product1(A,B,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[164591312,164599288]),
[] ).
fof(e_2_is_not_e_1,plain,
~ equalish(e_2,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164551480,plain,
~ equalish(e_2,e_1),
inference(rewrite,[status(thm)],[e_2_is_not_e_1]),
[] ).
cnf(173615848,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[173603920,164551480]),
[] ).
cnf(175549624,plain,
( product1(e_2,e_1,e_1)
| product1(e_2,e_1,e_3) ),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164527472,164531512,164570736,173615848]),
[] ).
fof(product1_left_cancellation,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164594944,plain,
( ~ product1(A,B,C)
| ~ product1(D,B,C)
| equalish(A,D) ),
inference(rewrite,[status(thm)],[product1_left_cancellation]),
[] ).
cnf(173648888,plain,
( ~ product1(A,B,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[164594944,164599288]),
[] ).
cnf(173657248,plain,
~ product1(e_2,e_1,e_1),
inference(resolution,[status(thm)],[173648888,164551480]),
[] ).
cnf(176688432,plain,
product1(e_2,e_1,e_3),
inference(resolution,[status(thm)],[175549624,173657248]),
[] ).
fof(e_3_is_not_e_1,plain,
~ equalish(e_3,e_1),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164505760,plain,
~ equalish(e_3,e_1),
inference(rewrite,[status(thm)],[e_3_is_not_e_1]),
[] ).
cnf(173943744,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[173603920,164505760]),
[] ).
cnf(173641144,plain,
( ~ product1(B,A,A)
| equalish(A,B) ),
inference(resolution,[status(thm)],[164594944,164599288]),
[] ).
fof(e_1_is_not_e_3,plain,
~ equalish(e_1,e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164547704,plain,
~ equalish(e_1,e_3),
inference(rewrite,[status(thm)],[e_1_is_not_e_3]),
[] ).
cnf(173998936,plain,
~ product1(e_3,e_1,e_1),
inference(resolution,[status(thm)],[173641144,164547704]),
[] ).
fof(element_3,plain,
group_element(e_3),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164535216,plain,
group_element(e_3),
inference(rewrite,[status(thm)],[element_3]),
[] ).
fof(qg1a,plain,
! [A,B,C,D] :
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164637120,plain,
( ~ product1(A,B,C)
| ~ product1(C,B,D)
| product2(D,A,B) ),
inference(rewrite,[status(thm)],[qg1a]),
[] ).
fof(product2_total_function2,plain,
! [A,B,C,D] :
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164619920,plain,
( ~ product2(A,B,C)
| ~ product2(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[product2_total_function2]),
[] ).
fof(product2_idempotence,plain,
! [A] : product2(A,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),
[] ).
cnf(164632152,plain,
product2(A,A,A),
inference(rewrite,[status(thm)],[product2_idempotence]),
[] ).
cnf(173701312,plain,
( ~ product2(A,A,B)
| equalish(A,B) ),
inference(resolution,[status(thm)],[164619920,164632152]),
[] ).
cnf(174086560,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[173701312,164505760]),
[] ).
cnf(174419952,plain,
( ~ product1(e_3,e_1,A)
| ~ product1(A,e_1,e_3) ),
inference(resolution,[status(thm)],[164637120,174086560]),
[] ).
cnf(176016280,plain,
~ product1(e_2,e_1,e_3),
inference(forward_subsumption_resolution__resolution,[status(thm)],[173943744,173998936,164527472,164535216,164570736,174419952]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[176688432,176016280]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(element_1,plain,(group_element(e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164527472,plain,(group_element(e_1)),inference(rewrite,[status(thm)],[element_1]),[]).
%
% fof(element_2,plain,(group_element(e_2)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164531512,plain,(group_element(e_2)),inference(rewrite,[status(thm)],[element_2]),[]).
%
% fof(product1_total_function1,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164570736,plain,(~group_element(A)|~group_element(B)|product1(A,B,e_1)|product1(A,B,e_2)|product1(A,B,e_3)),inference(rewrite,[status(thm)],[product1_total_function1]),[]).
%
% fof(product1_right_cancellation,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164591312,plain,(~product1(A,B,C)|~product1(A,D,C)|equalish(B,D)),inference(rewrite,[status(thm)],[product1_right_cancellation]),[]).
%
% fof(product1_idempotence,plain,(product1(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164599288,plain,(product1(A,A,A)),inference(rewrite,[status(thm)],[product1_idempotence]),[]).
%
% cnf(173603920,plain,(~product1(A,B,A)|equalish(A,B)),inference(resolution,[status(thm)],[164591312,164599288]),[]).
%
% fof(e_2_is_not_e_1,plain,(~equalish(e_2,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164551480,plain,(~equalish(e_2,e_1)),inference(rewrite,[status(thm)],[e_2_is_not_e_1]),[]).
%
% cnf(173615848,plain,(~product1(e_2,e_1,e_2)),inference(resolution,[status(thm)],[173603920,164551480]),[]).
%
% cnf(175549624,plain,(product1(e_2,e_1,e_1)|product1(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[164527472,164531512,164570736,173615848]),[]).
%
% fof(product1_left_cancellation,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164594944,plain,(~product1(A,B,C)|~product1(D,B,C)|equalish(A,D)),inference(rewrite,[status(thm)],[product1_left_cancellation]),[]).
%
% cnf(173648888,plain,(~product1(A,B,B)|equalish(A,B)),inference(resolution,[status(thm)],[164594944,164599288]),[]).
%
% cnf(173657248,plain,(~product1(e_2,e_1,e_1)),inference(resolution,[status(thm)],[173648888,164551480]),[]).
%
% cnf(176688432,plain,(product1(e_2,e_1,e_3)),inference(resolution,[status(thm)],[175549624,173657248]),[]).
%
% fof(e_3_is_not_e_1,plain,(~equalish(e_3,e_1)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164505760,plain,(~equalish(e_3,e_1)),inference(rewrite,[status(thm)],[e_3_is_not_e_1]),[]).
%
% cnf(173943744,plain,(~product1(e_3,e_1,e_3)),inference(resolution,[status(thm)],[173603920,164505760]),[]).
%
% cnf(173641144,plain,(~product1(B,A,A)|equalish(A,B)),inference(resolution,[status(thm)],[164594944,164599288]),[]).
%
% fof(e_1_is_not_e_3,plain,(~equalish(e_1,e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164547704,plain,(~equalish(e_1,e_3)),inference(rewrite,[status(thm)],[e_1_is_not_e_3]),[]).
%
% cnf(173998936,plain,(~product1(e_3,e_1,e_1)),inference(resolution,[status(thm)],[173641144,164547704]),[]).
%
% fof(element_3,plain,(group_element(e_3)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164535216,plain,(group_element(e_3)),inference(rewrite,[status(thm)],[element_3]),[]).
%
% fof(qg1a,plain,(~product1(A,B,C)|~product1(C,B,D)|product2(D,A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164637120,plain,(~product1(A,B,C)|~product1(C,B,D)|product2(D,A,B)),inference(rewrite,[status(thm)],[qg1a]),[]).
%
% fof(product2_total_function2,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164619920,plain,(~product2(A,B,C)|~product2(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[product2_total_function2]),[]).
%
% fof(product2_idempotence,plain,(product2(A,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP123-9.003.tptp',unknown),[]).
%
% cnf(164632152,plain,(product2(A,A,A)),inference(rewrite,[status(thm)],[product2_idempotence]),[]).
%
% cnf(173701312,plain,(~product2(A,A,B)|equalish(A,B)),inference(resolution,[status(thm)],[164619920,164632152]),[]).
%
% cnf(174086560,plain,(~product2(e_3,e_3,e_1)),inference(resolution,[status(thm)],[173701312,164505760]),[]).
%
% cnf(174419952,plain,(~product1(e_3,e_1,A)|~product1(A,e_1,e_3)),inference(resolution,[status(thm)],[164637120,174086560]),[]).
%
% cnf(176016280,plain,(~product1(e_2,e_1,e_3)),inference(forward_subsumption_resolution__resolution,[status(thm)],[173943744,173998936,164527472,164535216,164570736,174419952]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[176688432,176016280]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------